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Fixed point and selection theorems in hyperconvex spaces |
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| Authors: | M. A. Khamsi W. A. Kirk Carlos Martinez Yañ ez |
| Affiliation: | Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas 79968-0514 ; Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242-1419 ; Institute of Mathematics, Universidad Catolica de Valparaiso, Valparaiso, Chile |
| Abstract: | It is shown that a set-valued mapping |
| Keywords: | Hyperconvex metric spaces fixed points selection theorems fixed points |
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of a hyperconvex metric space 
which takes values in the space of nonempty externally hyperconvex subsets of 
always has a lipschitzian single valued selection 
which satisfies 
for all 
. (Here 
denotes the usual Hausdorff distance.) This fact is used to show that the space of all bounded 
-lipschitzian self-mappings of 
is itself hyperconvex. Several related results are also obtained.